I went through something similar during my divorce except it was my friends from long before my ex came into the picture that chose sides. The ex gave an Academy Award performance of the poor dumped victim and they fell for it. I felt extremely hurt and betrayed that my so-called friends would believe him and judge me.
After about a year, they saw his true colours and apologized to me, but it was too little, too late. He used their sympathy as a ploy to get information about me to the point of stalking me. They now have nothing to do with him and I have little to do with them.
Many times, when the ex stays involved with the friends, no matter which friends they are, it is not to be friends, but it is to serve their own vengeful purpose. His constant involvement in their lives caused me major problems in the divorce. They unknowingly would tell him things about me that I didn't want him to know. He totally used them for his own purposes.
I have never been one to stay friends with both sides. My Best friend left her husband a few years ago. While I liked him as a person, my loyalty is first to her and I wouldn't even think of pursuing a friendship with him. If I ran into him on the street, I would speak to him, be pleasant and have a casual conversation, but that's it.
I choose the people with whom I was friends first. I never went out of my way to contact the ex's friends, but he certainly did the complete opposite.
People not wanting to choose sides can unknowingly cause major harm or obstacles to an already stressful and sticky situation.